Under previously recognized conditions of stabilization (oxidation), acrylonitrile polymer carbon precursor fibers are subjected to low temperatures i.e. 220.degree.-250.degree. C. for relatively long periods of time in order to avoid too rapid an exotherm which leads to breakage of the tows. U.S. Pat. No. 3,412,062 is representative of the prior art which teaches the stabilization of such fibers for 24-50 hours at 220.degree. C. while preventing the fibers from shrinking more than 12% by applying tension thereto. In some instances, the fiber is allowed to stretch up to 36%.